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#1
Mar2108, 12:28 AM

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Hi. First post here. I have no formal math or physics training, but read popular books on physics and am pretty well read as far as that goes. Now for the question.
I'm fascinated by the Newton's Bucket problem and fortunately for me it's cleared my head of the 2 brothers paradox (one on earth, one in ship, ship ages) with regard to which one is considered moving and which is stationary. For a description of Newton's Bucket, here's a good one: http://wwwgroups.dcs.stand.ac.uk/~...on_bucket.html I've never liked the traditional idea that the brother that is considered moving (and therefore aging) is the one that is accelerating away because once acceleration stops and the ship continues at near light speed, the aging process continues yet the ship is only moving relative to the Earth and not accelerating away from it. Newton's Bucket solves that problem by inferring that the ship is moving near light speed relative to either the stars or some universal fabric that is static or almost static relative to the stars. Newton's bucket implies that if the universe were empty (I suppose this would include dark matter and energy) except for the bucket and a single observer, the bucket would seemingly have to behave strangely. For example, if the observer were spinning around the bucket (and the bucket around the observer) but both in the same direction as far as the two axis of rotation are concerned, the bucket could not be said to be spinning and therefore would not exhibit inertial forces or the resultant concave water. If the observer and bucket were spinning opposite to each other, then what? Would the water then become concave relative to the velocity of the observer? Or is a greater mass (or something else altogether) required such as massive galaxies? And if either or both are causing the water to become concave, then what exactly is causing it. I realize the simple answer is inertia, but this paradox implies that inertia would cease to exist in an empty universe and with the observer and bucket moving in the same direction or possibly in different directions as well. Inertia would have to cease to exist in an empty universe that contained only a bucket of water and a single observer moving in the same direction around it as there would be absolutely no frame of reference with regard to acceleration. With no inertia, one could not feel any effects of acceleration so if the bucket exploded, or the observer sneezed, which would move relative to the other, and which one would age when applied to the two brother paradox. Glad to have found this forum. 


#2
Mar2108, 05:14 AM

P: 3,967

The answer you seek is the article you linked to.
".....in simple terms, in a universe with no matter there is no gravity. Hence general relativity reduces to special relativity and now all observers agree when the rock system is spinning (i.e. accelerating). " In other words relativity says rotation is detectable even with one object in an empty universe. Of course this is hard to prove with an experiment, as we do not have a spare empty universe to try it out in :P Tha article also tries to lend some support to Mach's views (that all inertia is relative to the fixed stars): "In 1985 further progress by H Pfister and K Braun showed that sufficient centrifugal forces would be induced at the centre of the hollow massive sphere to cause water to form a concave surface in a bucket which is not rotating with respect to the distant stars. Here at last was a form of the symmetry that Mach was seeking. " A counter argument is this: Rotate a bucket clockwise (when looking from above) so that the water contained within it has a concave surface. Define the bucket as stationary and atribute the concave surface of the water to the gravitational influence of the all the universes stars orbiting anticlockwise around said bucket. Now place another rotating bucket alongside the first bucket while the water within it is still spinning. If the first bucket is exactly at the axis of the spinning universe, then the second bucket is not and yet the lowest point of the water in the second bucket is exactly at the centre of its spinning surface. Mach's principle seems to fall apart as soon as we introduce a second bucket. 


#3
Mar2108, 06:54 AM

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Welcome to these Forums Buckethead, glad too that you found us!
Mach's Principle might not rely on just gravitational influences, as it would in GR. In the Brans Dicke theory an extra scalar field coupled to matter endows fundamental particles with inertial mass. Thus introducing the second bucket proves that Mach's Principle is incompatible with GR but it may not be incompatible with an alternative gravitational theory. Garth 


#4
Mar2108, 06:54 AM

P: 303

Newton's Bucket
"Newton's Bucket" only works in the presence of gravity as kev pointed out.
That said  the pressure in the water increases linearly from 0 to [itex] \rho gh[/itex] no matter where you check from top to bottom. When the bucket/water is spinning uniformly, a new force is added to keep the water from travelling along a linear path. This new force creates another linear pressure gradient that starts from the center of the bucket and increases as you move away from the axis of rotation. The product of the two orthogonal linear pressure gradients leads to a parabolic pressure profile at any fixed height. The water surface assumes a parabolic shape to support both linear pressure gradients simultaneously. Regards, Bill 


#5
Mar2108, 05:33 PM

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#6
Mar2108, 05:46 PM

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#7
Mar2108, 06:08 PM

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#8
Mar2108, 07:32 PM

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Buckethead:
I would expect any spinning object to experience stresses because of the spin, and this would happen in any sort of universe, regardless of gravity. 


#9
Mar2108, 08:26 PM

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Please realize though that I am also trying to figure out here what is an "empty universe". Is it simply a universe void of matter? Of dark matter and dark energy? Of virtual particles? Also, I'm not completely convinced that it's matter that is the real reference point for a spinning object and it's associated stresses (acceleration). It could also be that even an empty universe has some kind of inherent frame of reference that defines that it is static and not moving regardless of whether or not it contains matter, dark matter, and/or dark energy. If this is the case, then I would think a spinning object would still show rotational forces acting on it even in a massless universe. But if this is the case, then it would turn the physics world upside down I would think. 


#10
Mar2108, 09:08 PM

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Buckethead:
Firstly, rotation can only be defined for an extended object. A point cannot rotate. So the parts of the extended object have proper spatial relationships with each other and provide a frame in which to define rotation independently of any external reference. I can choose the centre of the rotation as the origin of a frame, and then define a tangential velocity of a piece away from the centre. The same argument might well do for the acceleration case, but you should bear in mind that your one single object in the universe can only accelerate by ejecting some matter, in which case we have more than one object and the argument short circuits. [edit] Rereading this, I'm not 100% convinced by my logic, it would be interesting to hear other views. 


#11
Mar2108, 09:32 PM

P: 303

Regards, Bill 


#12
Mar2108, 10:07 PM

P: 3,967

Hi,
I am aware that Einstein himself concluded that Mach's principle is incompatible with GR as demonstrated by this quote: "This certainly was a clever idea on Einstein's part, but by June 1918 it had become clear that the De Sitter world does not contain any hidden masses and is thus a genuine counterexample to Mach's principle. Another one of Einstein's attempts to relativize all motion had failed. Einstein thereupon lost his enthusiasm for Mach's principle. He accepted that motion with respect to the metric field cannot always be translated into motion with respect to other matter." from this article http://science.jrank.org/pages/11027...elativity.html However, after further reflection Mach's principle is not dismissed by the simple counter example I gave. In that example the second bucket would appear to be rotating along with the distant stars from the point of view of an observer stationary with respect to the water in the first bucket. The second bucket would not therefore be submitted to the "spiralling spacetime" that the water in the first bucket is subjected to, because the second bucket is comoving with the spiralling spacetime/ gravitational field. A clearer (and fairer) example would be to place the first bucket at the centre of a large rotating turntable. An observer on the turntable could place a second bucket near the rim of the turntable and observe that the water in the second bucket is at rest with with respect to the water of the first bucket and that the water in the second bucket is piled up asymmetrically on the side furthest from the centre of the turntable. If the water in the second bucket is spinning then the centre of the concave depression would indeed be offset from the centre of the bucket. In this fairer second example, Mach's principle does not fail. Can anyone think of a simple example (that is easy to visualise), where Mach's principle fails? 


#13
Mar2108, 10:14 PM

P: 303

The spherical blob of water you mentioned only remains so because of surface tension. If that blob of water were to rotate about some axis, there would have to be more surface area in a plane perpendicular to the axis of rotation to keep the forces in equilibrium  leading to an ellipsoidal shape. Oddly, a spherical blob of water travelling at a significant fraction of the speed of light would also look like an ellipsoid to a stationary observer  but for a different reason. Regards, Bill 


#14
Mar2108, 10:34 PM

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#15
Mar2108, 10:53 PM

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When you drive to work, accelerating and breaking at junctions and experiencing "centrifugal force" as you go round corners, the whole journey can be explained in terms of gravitational fields and complicated accelerations of everything in the universe while you have remained stationary throughout the entire journey. Now this point of view is necessary or we have to accept a notion of absolute motion which is incompatible with Relativity. Occam's razor and even considerations of conservation of energy are not strong enough arguments to support a notion of absolute motion or acceleration. 


#16
Mar2108, 11:26 PM

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#17
Mar2108, 11:30 PM

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Kev:



#18
Mar2108, 11:35 PM

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If I define a frame centred on one brick, the other is rotating around it. If a system is revolving, it must have spatial extension, and so you can define the motion of one part relative to the other parts. No absolute space required. 


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